WO2023157118A1 - Dispositif de calcul sécurisé, procédé de calcul sécurisé et programme - Google Patents

Dispositif de calcul sécurisé, procédé de calcul sécurisé et programme Download PDF

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Publication number
WO2023157118A1
WO2023157118A1 PCT/JP2022/006128 JP2022006128W WO2023157118A1 WO 2023157118 A1 WO2023157118 A1 WO 2023157118A1 JP 2022006128 W JP2022006128 W JP 2022006128W WO 2023157118 A1 WO2023157118 A1 WO 2023157118A1
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Prior art keywords
window frame
string
frame flag
flag string
value
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PCT/JP2022/006128
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English (en)
Japanese (ja)
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弘貴 須藤
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日本電信電話株式会社
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    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09C—CIPHERING OR DECIPHERING APPARATUS FOR CRYPTOGRAPHIC OR OTHER PURPOSES INVOLVING THE NEED FOR SECRECY
    • G09C1/00—Apparatus or methods whereby a given sequence of signs, e.g. an intelligible text, is transformed into an unintelligible sequence of signs by transposing the signs or groups of signs or by replacing them by others according to a predetermined system
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/40—Network security protocols

Definitions

  • the present invention relates to a secure computing device, a secure computing method, and a program for securely computing a database.
  • the Window function is a function that groups records by key attributes, and performs aggregation within a "window" of a specified width based on each row. For example, in the case of a total for one column before and after, the input and output are as shown in Table 1. Note that the values in different groups are not summed up at this time. There is a Group by function that is similar to the Window function, but the Group by function aggregates each group into a single value, while the Window function aggregates each row within the window frame and outputs the result. different in that Patent Document 1 and Non-Patent Document 1 are available as conventional technologies related to Group By.
  • the secure computing device of the present invention is a secure computing device that performs calculations while concealing a database containing a key string k ⁇ that is an attribute string and a data string v ⁇ that is a value string.
  • the group flag string g ⁇ represents a vector whose value is 1 at the position where the value of the key string changes and whose value is 0 at other positions.
  • [[x]] denote the share of value x by Shamir secret sharing
  • i denote the current row number, s the window start position, t the window end position, and the key columns and Assume that the number of rows in the data string is l, and the current row number i is incremented by 1 each time all flag string generation processing is completed within the range of 0 to less than l.
  • the secure computing device of the present invention includes a first half window frame flag string generator, a second half window frame flag string generator, a window frame flag string generator, an inverted window frame flag string generator, a share converter, and a sum-of-products Includes calculation part.
  • the first-half window frame flag string generator extracts the s+1-th element to the i-th element of ⁇ g ⁇ ⁇ for the vector subVector ( ⁇ g ⁇ ⁇ ,s+1,i), each position from the end A bit string obtained by ORing all bits up to is generated as the first half window frame flag string ⁇ w f ⁇ ⁇ .
  • the second half window frame flag string generator extracts the i+1th to tth elements of ⁇ g ⁇ ⁇ for the vector subVector ( ⁇ g ⁇ ⁇ , i+1, t), from the beginning to each position A bit string obtained by ORing all bits is generated as the second half window frame flag string ⁇ w l ⁇ ⁇ .
  • the window frame flag string generator combines the first half window frame flag string ⁇ w f ⁇ ⁇ from the front and the second half window frame flag string ⁇ w l ⁇ ⁇ from the back, with ⁇ 0 ⁇ interposed to combine them. Generates ⁇ w ⁇ ⁇ .
  • the reversed window frame flag string generator generates a reversed window frame flag string ⁇ w' ⁇ ⁇ by performing a NOT operation on the window frame flag string ⁇ w ⁇ ⁇ .
  • the share conversion unit converts the reversed window frame flag string ⁇ w' ⁇ ⁇ to the reversed window frame flag string [[w' ⁇ ]].
  • the sum-of-products operation part extracts the elements from s to t of the data string [[v' ⁇ ] ] sorted in ascending order. t) and the inverted window frame flag string [[w' ⁇ ]].
  • the secure computing device of the present invention it is possible to calculate the sum operation of the window function with low-cost operations.
  • FIG. 2 is a block diagram showing the functional configuration of the secure computing device according to the first embodiment
  • FIG. 4 is a flowchart showing the operation of the secure computing device of the first embodiment
  • FIG. 3 is a block diagram showing the functional configuration of a secure computing device according to Modification 1
  • 10 is a flowchart showing the operation of the secure computing device of Modification 1; The figure which shows the functional structural example of a computer.
  • c ⁇ max(a,b) is calculated in plaintext and outputs the plaintext a or b, whichever has the larger value.
  • c ⁇ min(a,b) outputs the smaller value of plaintext a and b in plaintext calculation.
  • Secret sharing is an encryption method that divides data into multiple values and distributes them to multiple parties.
  • the secure computing device of the following embodiment encrypts data by (k, n) threshold secret sharing.
  • (k,n) threshold secret sharing means that the data is divided into n random values (called shares), the original data can be recovered by collecting more than k shares, and the original data can be recovered from less than k shares.
  • the secure computing devices of the following embodiments use Shamir secret sharing (reference non-patent document 1) and replication secret sharing (reference non-patent documents 2 and 3).
  • Reference non-patent document 1 Adi Shamir. How to share a secret. Communications of the ACM, Vol. 22, No. 11, pp. 612-613, 1979.
  • Reference non-patent document 2 Mitsuru Ito, Akira Saito, and Takao Nishizeki. Secret sharing scheme realizing general access structure. Electronics and Communications in Japan (Part III: Fundamental Electronic Science), Vol. 72, No. 9, pp. 56 -64, 1989.)
  • Reference Non-Patent Document 3 Ronald Cramer, Ivan Damgard, and Yuval Ishai. Share conversion, pseudorandom secret-sharing and applications to secure computation. In Theory of Cryptography Conference, pp. 342-362.
  • the share of the value x by Shamir secret sharing is represented as [[x]].
  • the share of the value x by replication secret sharing is expressed as ⁇ x ⁇ . Since replication secret sharing is particularly efficient for processing 1-bit data, it is used selectively in the following examples. Also, the value obtained by sharing the permutation ⁇ is expressed as ⁇ >.
  • the OR operation is an operation that inputs ciphertexts ⁇ a ⁇ and ⁇ b ⁇ of 1-bit values a and b and outputs a ciphertext of the calculation result c of aORb, and is described as follows.
  • PrefixOR is an operation that returns a bit string obtained by ORing all bits from the beginning to each position for the bit string b ⁇ .
  • the output is c ⁇
  • SuffixOR is an operation that returns a bit string obtained by ORing all bits from the end of c ⁇ to each position.
  • a secure stable sort is a protocol for stable sorting of vectors.
  • the secure stable sort consists of the following algorithms. ⁇ > ⁇ GenPerm([[k ⁇ ]]): Outputs a permutation ⁇ that stably sorts the key string k ⁇ in ascending order. [[v' ⁇ ]] ⁇ Sort( ⁇ >, [[v ⁇ ]]): Outputs [[v' ⁇ ]] sorted by applying ⁇ to v ⁇ .
  • Reference Non-Patent Document 4 and the like are known as a high-speed mounting method for realizing this.
  • the second line shows a process of stably encrypting the key string [[k ⁇ ]] by ⁇ and outputting the result of sorting [[k′ ⁇ ]].
  • the third line shows a process of performing anonymity stable sorting on the data string [[v ⁇ ]] by ⁇ and outputting the sort result [[v′ ⁇ ]].
  • the fourth line sets the top value ⁇ eq ⁇ ⁇ 0 of the vector ⁇ eq ⁇ ⁇ to ⁇ 0 ⁇ , and sets the top value ⁇ g ⁇ ⁇ 0 of the group flag string ⁇ g ⁇ ⁇ to ⁇ 1 ⁇ . processing.
  • the 5th line indicates that the processing of the 6th and 7th lines is repeated.
  • Line 6 replaces i-th value ⁇ eq ⁇ ⁇ i of vector ⁇ eq ⁇ ⁇ with Eq([[k ⁇ ]] i-1 ,[[k ⁇ ]] i ), i.e. i-1 If the value [[k ⁇ ]] i ⁇ 1 and the i-th value [[k ⁇ ]] i are equal, 1 is given, and if they are different, 0 is given. Therefore, the vector eq ⁇ is a vector characterized by a series of 1s until reaching the point where the value of the key string changes, a point of 0 at the point where the value of the key string changes, and a series of 1s until the next point where the value of the key string changes. is.
  • Line 7 sets the i-th value ⁇ g ⁇ ⁇ i of the group flag string ⁇ g ⁇ ⁇ to Not( ⁇ eq ⁇ ⁇ i ). represents a vector whose value is 1 and whose value is 0 at other positions.
  • the 8th line indicates the end of the iteration process, and the 9th line is the output of Algorithm 1: grouped key column [[k' ⁇ ]], grouped data column [[v' ⁇ ]] , represents the group flag sequence ⁇ g ⁇ ⁇ .
  • Algorithm 2 shows the details of the method for generating the window frame flag string for executing the window function on secure computation, which is a method unique to the present invention.
  • Input Group flag string ⁇ g ⁇ ⁇ , current line number i, window frame start position s, window frame end position t (however, s ⁇ i ⁇ t)
  • Output window frame flag string ⁇ w ⁇ ⁇ 1: ⁇ w f ⁇ ⁇ SuffixOr(subVector( ⁇ g ⁇ ⁇ ,s+1,i)) 2: ⁇ w l ⁇ ⁇ PrefixOr(subVector( ⁇ g ⁇ ⁇ ,i+1,t)) 3: ⁇ w ⁇ ⁇ w f ⁇ ⁇
  • the first line of Algorithm 2 is a vector subVector( ⁇ g ⁇ ⁇ ,s+1 , i), SuffixOr, ie, a bit string obtained by ORing all bits from the end to each position, is generated as the first
  • the second line is PrefixOr , that is, the beginning to each position is generated as the second half window frame flag string ⁇ w l ⁇ ⁇ . Therefore, if a position where the value of the key string changes appears on the way from the beginning to the end, all the elements located at the end from this position will be 1, so 0,...,0,1,...,1 Such a result is obtained.
  • Lines 3 and 4 indicate that ⁇ w ⁇ ⁇ is generated and output by combining ⁇ w f ⁇ ⁇ from the front, ⁇ w l ⁇ ⁇ from the back, and ⁇ 0 ⁇ in between. . That is, ⁇ 0 ⁇ corresponds to the current line number.
  • the vector w ⁇ has the characteristic that it indicates the value 0 for elements belonging to the group containing the current row number, and the value 1 for elements belonging to a group different from the group containing the current row number. For example, if the element corresponding to the current line number is represented by > ⁇ , then the vector w ⁇ is 1,...,1,0,...,>0 ⁇ ,...,0,1,...,1 An example output is possible.
  • the second line indicates that the processing up to the 9th line is repeatedly executed.
  • the 3rd line is i-poffset, that is, the position offset from the current line number i by the window frame start position offset poffset is set as the window frame start position s, and all exceptions where i-poffset is 0 or less are treated as 0. To do so, the process of calculating the window frame start position s as s ⁇ max(i-poffset, 0) is shown.
  • i + foffset that is, the position offset by the window frame end position offset foffset from the current line number i is the window frame end position t
  • i + foffset is l-1 or more
  • the fifth line shows processing for calculating the window frame flag string ⁇ w ⁇ ⁇ by Algorithm 2.
  • the sixth line shows processing for generating a reversed window frame flag string ⁇ w' ⁇ ⁇ by performing NOT operation on the window frame flag string ⁇ w ⁇ ⁇ .
  • the 7th line shows the process of converting ⁇ w' ⁇ ⁇ , which is the shared secret sharing share, into the share [[w' ⁇ ]] of Shamir secret sharing.
  • the 7th line is performed to execute the PSum processing in the following 8th line.
  • the eighth line is a subVector ([[v' ⁇ ]],s,t that extracts the elements from the window frame start position s to the window frame end position t of the data string [[v' ⁇ ]] sorted in ascending order ) and [[w' ⁇ ]].
  • the value remains as the product only for the positions of the aggregation target, and the other products are all 0, so the aggregation result column [[u ⁇ ]] indicates the result of the Sum operation for the aggregation target.
  • the ninth line shows the end of the iterative process, and the tenth line shows the process of outputting the grouped key string [[k' ⁇ ]] and aggregation result string [[u ⁇ ]].
  • the data columns are sorted in ascending order within the group.
  • ⁇ w ⁇ ⁇ which is a flag string, is generated such that 0 is set for positions to be counted and 1 is set for positions that are not.
  • ⁇ g ⁇ ⁇ is a flag string in which the element at the end of the group is indicated by 1 in Non-Patent Document 1, but if it is regarded as a flag associated with the boundary of the group, it is regarded as a bit string in which the group boundary is indicated by 1. can be fixed.
  • Algorithm 2 by taking Suffix/Prefix OR in the vertical direction, it is possible to generate a flag string in which the elements beyond the group boundary are 1. However, the current row is always counted, so the initial value is 0.
  • ⁇ w ⁇ ⁇ is a flag string in which 0 is the position to be tallied and 1 is not.
  • the secure computing device 1 of this embodiment includes an input data storage unit 10A, a first half window frame flag string generator 10, a second half window frame flag string generator 11, and a window frame flag string generator 12. , an inverted window frame flag string generation unit 13, a share conversion unit 14, a sum-of-products operation unit 15, and an output data storage unit 10B.
  • the input data storage unit 10A stores in advance data to be input to the secure computing device. In this embodiment, it is assumed that Algorithm 1 has already been executed, and the input data storage unit 10A stores a grouped key string [[k' ⁇ ]], a grouped data string [[v' ⁇ ]], It remembers the group flag sequence ⁇ g ⁇ ⁇ .
  • the input data storage unit 10A also stores in advance a window frame start position offset poffset and a window frame end position offset foffset, which are parameters arbitrarily set by the user.
  • the input data storage unit 10A stores a key string [[k ⁇ ]], a data string [[v ⁇ ]], a window frame start position offset poffset, a window frame
  • the end position offset foffset should be stored in advance.
  • the first-half window frame flag string generator 10 executes the 3rd to 5th lines of Algorithm 3 (the 1st line of Algorithm 2 referenced by the 5th line) according to the repetition condition of the 2nd line of Algorithm 3 .
  • the first half window frame flag string generator 10 acquires the window frame start position s and the window frame end position t, and extracts the elements from the s+1-th element of ⁇ g ⁇ ⁇ to the i-th element.
  • the vector subVector ( ⁇ g ⁇ ⁇ , s+1, i) consisting of the following, a bit string obtained by ORing all bits from the end to each position is generated as the first half window frame flag string ⁇ w f ⁇ ⁇ (S10 ).
  • the second half window frame flag string generating unit 11 executes the 3rd to 5th lines of Algorithm 3 (the 2nd line of Algorithm 2 referred to by the 5th line) according to the repetition condition of the 2nd line of Algorithm 3 .
  • the second half window frame flag string generator 11 obtains the window frame start position s and the window frame end position t, and extracts the i+1-th to t-th elements of ⁇ g ⁇ ⁇ .
  • the vector subVector ( ⁇ g ⁇ ⁇ , i+1, t)
  • a bit string obtained by ORing all bits from the beginning to each position is generated as the second half window frame flag string ⁇ w l ⁇ ⁇ (S11).
  • the window frame flag string generator 12 executes the 5th line of Algorithm 3 (the 3rd line of Algorithm 2 referenced by the 5th line) according to the repeat condition of the 2nd line of Algorithm 3 .
  • the window frame flag string generation unit 12 joins the first half window frame flag string ⁇ w f ⁇ ⁇ from the front and the second half window frame flag string ⁇ w l ⁇ ⁇ from the rear, sandwiching ⁇ 0 ⁇ . Thus, a window frame flag string ⁇ w ⁇ ⁇ is generated (S12).
  • the inversion window frame flag string generator 13 executes the sixth line of Algorithm 3 according to the repetition condition of the second line of Algorithm 3 .
  • the reversed window frame flag string generator 13 generates a reversed window frame flag string ⁇ w' ⁇ ⁇ by performing a NOT operation on the window frame flag string ⁇ w ⁇ ⁇ (S13).
  • the share conversion unit 14 converts the reversed window frame flag string ⁇ w' ⁇ ⁇ into the reversed window frame flag string [[w' ⁇ ]] (S14).
  • the sum-of-products operation unit 15 executes the 8th line of Algorithm 3 according to the repetition condition of the 2nd line of Algorithm 3 .
  • the sum-of-products operation unit 15 extracts the elements from s to t of the data string [[v' ⁇ ]] obtained by sorting the data string [[v ⁇ ]] in ascending order. ⁇ ]], s, t) and the inverted window frame flag string [[w' ⁇ ]] are sum-of-products (S15).
  • the output data storage unit 10B stores [[k' ⁇ ]] and [[u ⁇ ]], which are the outputs of Algorithm 3 .
  • the secure computing device includes a database 2 composed of pre-anonymized data, a data anonymizing unit 3 for anonymizing the data in the database 2, and the same processing as the secure computing device 1. (secure computing device 100 of modified example 1, steps S3 and S1).
  • the apparatus of the present invention includes, for example, a single hardware entity, which includes an input unit to which a keyboard can be connected, an output unit to which a liquid crystal display can be connected, and a communication device (for example, a communication cable) capable of communicating with the outside of the hardware entity.
  • a communication device for example, a communication cable
  • CPU Central Processing Unit, which may include cache memory, registers, etc.
  • memory RAM and ROM external storage device such as hard disk
  • input unit, output unit, communication unit a CPU, a RAM, a ROM, and a bus for connecting data to and from an external storage device.
  • the hardware entity may be provided with a device (drive) capable of reading and writing a recording medium such as a CD-ROM.
  • a physical entity with such hardware resources includes a general purpose computer.
  • the external storage device of the hardware entity stores the programs necessary for realizing the functions described above and the data required for the processing of these programs (not limited to the external storage device; It may be stored in a ROM, which is a dedicated storage device). Data obtained by processing these programs are appropriately stored in a RAM, an external storage device, or the like.
  • each program stored in an external storage device or ROM, etc.
  • the data necessary for processing each program are read into the memory as needed, and interpreted, executed and processed by the CPU as appropriate.
  • the CPU realizes a predetermined function (each component expressed as above, . . . unit, . . . means, etc.).
  • a program that describes this process can be recorded on a computer-readable recording medium.
  • Any computer-readable recording medium may be used, for example, a magnetic recording device, an optical disk, a magneto-optical recording medium, a semiconductor memory, or the like.
  • magnetic recording devices hard disk devices, flexible disks, magnetic tapes, etc., as optical discs, DVD (Digital Versatile Disc), DVD-RAM (Random Access Memory), CD-ROM (Compact Disc Read Only Memory), CD-R (Recordable) / RW (ReWritable), etc., MO (Magneto-Optical disc) etc. as a magneto-optical recording medium, EEP-ROM (Electrically Erasable and Programmable-Read Only Memory) etc. as a semiconductor memory can be used.
  • EEP-ROM Electrical Erasable and Programmable-Read Only Memory
  • this program is carried out, for example, by selling, transferring, lending, etc. portable recording media such as DVDs and CD-ROMs on which the program is recorded.
  • the program may be distributed by storing the program in the storage device of the server computer and transferring the program from the server computer to other computers via the network.
  • a computer that executes such a program for example, first stores the program recorded on a portable recording medium or the program transferred from the server computer once in its own storage device. Then, when executing the process, this computer reads the program stored in its own recording medium and executes the process according to the read program. Also, as another execution form of this program, the computer may read the program directly from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to this computer. Each time, the processing according to the received program may be executed sequentially. In addition, the above-mentioned processing is executed by a so-called ASP (Application Service Provider) type service, which does not transfer the program from the server computer to this computer, and realizes the processing function only by its execution instruction and result acquisition. may be It should be noted that the program in this embodiment includes information that is used for processing by a computer and that conforms to the program (data that is not a direct instruction to the computer but has the property of prescribing the processing of the computer, etc.).
  • ASP
  • a hardware entity is configured by executing a predetermined program on a computer, but at least part of these processing contents may be implemented by hardware.

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Abstract

L'invention concerne un dispositif de calcul sécurisé comprenant : une première unité de génération de colonne d'indicateurs de trame de demi-fenêtre qui génère, en tant que \{wf→\}, une chaîne de bits obtenue, en tenant compte de subVector (\{g→\}, s+1, i), par l'exécution d'une opération OU sur l'ensemble des bits, de la fin jusqu'à chaque position ; une dernière unité de génération de colonne d'indicateurs de trame de demi-fenêtre qui génère, en tant que \{wl→\}, une chaîne de bits obtenue, en tenant compte de subVector(\{g→\}, i+1, t), par l'exécution d'une opération OU sur l'ensemble des bits, de la tête jusqu'à chaque position ; une unité de génération de colonne d'indicateur de trame de fenêtre qui génère \{w→\} en couplant \{wf→\} et \{wl→\} ; une unité de génération de colonne d'indicateurs de trame de fenêtre inversée qui génère \{w'→\} en effectuant une opération NON sur \{w→\} ; une unité de conversion de partage qui convertit \{w'→\} en [[w'→]] ; et une unité d'opération de somme de produits qui exécute une opération de somme de produits de subVector([[v' →]], s, t) et [[w'→]].
PCT/JP2022/006128 2022-02-16 2022-02-16 Dispositif de calcul sécurisé, procédé de calcul sécurisé et programme WO2023157118A1 (fr)

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